Find the value of k for which the roots alpha,beta of the equation x^2-6x+k=0 satisfy the relation 2 alpha +3 - Maths - Complex Numbers and Quadratic Equations

Question

Find the value of k for which the roots alpha,beta of the equation
x^2-6x+k=0 satisfy the relation 2 alpha +3 beta=20

Gursheen Kaur · Accepted Answer

Dear Student,Solution)Given   x2-6x+k=0α and β are the zeroes of given polynomial
⇒α + β=-(-6)1=6
(i)                αβ=k1=k
(ii)Now, 2α+3β=20
(iii) {given}Multiply (i) by 2 2α + 2β=122α + 3β=20-   -        -____________         -β=-8            β=8Put in (i) ,we get,α + β=6α + 8=6α =6-8α =-2Put α and  β values in (ii), we get,(-2)(8)=kor k=-16Regards!

Find the value of k for which the roots alpha,beta of the equation x^2-6x+k=0 satisfy the relation 2 alpha +3 beta=20